Structure of General Servers in Multiclass Queueing Networks

Abstract

Stability of queueing networks is a fundamental issue which has to be addressed before system capacity can be determined. However, due to the dependence among job classes, determining the stability region of a queueing network is intricate. In this paper, we consider the stability problem through the perspective of sample paths and generalize the concept of servers in multiclass queueing networks. The general servers have similar impacts on the system stability as physical stations and a queueing network is pathwise stable if and only if the effective traffic intensity of every general server does not exceed one. Since the identifying of general servers relies on the examinations of sample paths and may be intricate, rather than focusing on the identification of them, we employ the principle and concept to investigate the properties of queueing network stability in general settings. Through case studies, we show that the stability of queueing networks as well as the structure of general servers is sensitive and depends on various factors, including the distributions of interarrival and service times. Due to the computational complexity, although it may not be practical to determine the stability of a queueing network by identifying all general servers, through the concept we can show that queueing systems operating under practical service disciplines (i.e., WIP-dependent service disciplines, where WIP means Work-in-Progress) are always pathwise stable if every physical station has sufficient capacity.